I imagine myself in the victim's place, hearing a loud shout, turning, seeing the knife, throwing the guy, pinning him, and taking his knife -- just like in the dojo. Except that, in reality, I ignore mentally ill homeless people too. I don't make eye contact, and I can see myself behaving just like the victim did, regardless of how perceptive I think I am.

That woman made a mistake by not respecting the environment - in this case, an potentially aggressive homeless guy who could do her harm.

She went into denial mode and continued walking without acknowledging what's going on around her.

In these situations, you need to walk a middle ground.

Sometimes you need to say Hello, sometimes you might give them a buck, or you may choose not to, but no matter what you do, even if you ignore them, always keep them in your peripheral vision.

Sure you may not see exactly what the expression on their face is, but you'll spot a movement immediately.

They will also notice the fact that you are monitoring them and will think twice before doing anything.

This "looking-past-the-person-but-not-directly-at-them"

tactic is something that I use all the time.

If some macho tough guy starts playing a staring game in a bus, I just do the same thing. I don't clash with his stare, but I look just past him, like I'm looking outside the window, but yet he knows that I monitor him.